稀疏矩阵向量乘（SpMV）在线性系统的求解问题中具有重要意义，是科学计算和工程实践中的核心问题之一，其性能高度依赖于稀疏矩阵的非零分布。稀疏对角矩阵是一类特殊的稀疏矩阵，其非零元素按照对角线的形式密集排列。针对稀疏对角矩阵，在GPU平台上提出的多种存储格式虽然使SpMV性能有所提升，但仍存在零填充和负载不平衡的问题。针对上述问题，提出了一种DRM存储格式，利用基于固定阈值的矩阵划分策略和基于迭代归并的矩阵重构策略，实现了少量零填充和块间负载平衡。实验结果表明，在NVIDIA Tesla V100平台上，相比于DIA、HDC、HDIA和DIA-Adaptive格式，在时间性能方面，该存储格式分别取得了20.76,1.94,1.13和2.26倍加速;在浮点计算性能方面，分别提高了1.54,5.28,1.13和1.94倍。

Sparse matrix vector multiplication (SpMV) is of great significance in the solution of linear systems, and is one of the core problems in scientific computing and engineering practice. Its performance highly depends on the non-zero distribution of sparse matrices. Sparse diagonal matrices are a special type of sparse matrices, whose non-zero elements are densely arranged in the form of diagonals. For sparse diagonal matrices, scholars have proposed various storage formats on the GPU platform, which have improved SpMV performance, but still suffer from zero padding and load imbalance issues. To address these issues, a DRM (Divide-Rearrange & Merge) storage format is proposed. This format uses matrix partitioning strategies based on fixed threshold values and matrix reconstruction strategies based on iterative merging to achieve sparse zero padding and load balancing between blocks. Experimental results show that on the NVIDIA Tesla V100 platform, compared to DIA, HDC, HDIA, and DIA-Adaptive formats, the time performance is accelerated  by 20.76, 1.94, 1.13, and 2.26 times, respectively, and the floating point performance is improved by 1.54, 5.28, 1.13, and 1.94 times, respectively.


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